Question: Solve for $x$ and $y$ using elimination. ${-3x-3y = -30}$ ${2x+3y = 29}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-x = -1$ $\dfrac{-x}{{-1}} = \dfrac{-1}{{-1}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-3x-3y = -30}\thinspace$ to find $y$ ${-3}{(1)}{ - 3y = -30}$ $-3-3y = -30$ $-3{+3} - 3y = -30{+3}$ $-3y = -27$ $\dfrac{-3y}{{-3}} = \dfrac{-27}{{-3}}$ ${y = 9}$ You can also plug ${x = 1}$ into $\thinspace {2x+3y = 29}\thinspace$ and get the same answer for $y$ : ${2}{(1)}{ + 3y = 29}$ ${y = 9}$